Theorem 3ad2antl1 1185

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)

Hypothesis

Ref	Expression
3ad2antl.1	|- ( ( ph /\ ch ) -> th )

Assertion

Ref	Expression
3ad2antl1	|- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )

Proof of Theorem 3ad2antl1

Step	Hyp	Ref	Expression
1		3ad2antl.1	. . 3 |- ( ( ph /\ ch ) -> th )
2	1	adantlr 477	. 2 |- ( ( ( ph /\ ta ) /\ ch ) -> th )
3	2	3adantl2 1180	1 |- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1004

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1006

This theorem is referenced by:  acexmid  6017  f1oen4g  6925  f1dom4g  6926  ordiso2  7234  addlocpr  7756  distrlem1prl  7802  distrlem1pru  7803  ltsopr  7816  addcanprlemu  7835  fzo1fzo0n0  10422  pfxsuffeqwrdeq  11279  prodfap0  12107  prodfrecap  12108  muldvds2  12379  dvds2add  12387  dvds2sub  12388  dvdstr  12390  qusaddvallemg  13417  mulgnnsubcl  13722  mulgpropdg  13752  ringidss  14044  lmodprop2d  14364  cnpnei  14945  upxp  14998  lgsval4lem  15742  clwwlkccatlem  16253  clwwlkccat  16254